Cuda 8.0, Fedora 25, gcc stddef.h nullptr, GTX1060
I found the root problem, it was an incompatibility with C++ 11. So passing in a different standard along with compiling the CUDA kernel manually did the trick. Here is the command I ran (I got it from an output linked above):

/usr/local/cuda/bin/nvcc \
-arch=sm_61 -Xcompiler -std=c++98 --cubin \
"/usr/share/blender/2.78/scripts/addons/cycles/kernel/kernels/cuda/kernel.cu" \
-o "/home/user/.config/blender/2.78/cache/cycles_kernel_sm61_D8F831DA74C0363DC018432CF25F3AD8.cubin" \
-m64 --ptxas-options="-v" --use_fast_math -DNVCC -D__KERNEL_CUDA_VERSION__=80 \
-I"/usr/share/blender/2.78/scripts/addons/cycles/kernel"


Which did give me this warning:

cc1: warning: command line option ‘-std=c++98’ is valid for C++/ObjC++ but not for C


However, this doesn't seem to affect Blender's ability to use my video card. I saw a near 50% improvement in render times on the file I have been working on.

For reference, I found these pages that helped me finally hunt down a solution:

Nvidia forum post, CUDA using wrong GCC

Arch Linux bug report

Cplusplus.com forum post